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A Simple Method to Model a Continuous Glucose Monitoring Signal
Proceedings of the 20th World Congress The International Federation of Congress Automatic Control Proceedings of the 20th World Proceedings of the 20th World Congress Available online at www.sciencedirect.com Proceedings of the 20th9-14, World Toulouse, France, July 2017 The International Federation of Congress Automatic Control The International Federation of Automatic Control Proceedings of the 20th9-14, World The International Federation of Congress Automatic Control Toulouse, France, July 2017 Toulouse, France,Federation July 9-14, 2017 The International of Automatic Control Toulouse, France, July 9-14, 2017 Toulouse, France, July 9-14, 2017
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A Simple Method to Model a Continuous Glucose Monitoring Signal IFAC PapersOnLine 50-1 (2017) 8775–8780 A Simple Method to Model a Continuous Glucose Monitoring Signal A Method to a Glucose Monitoring Signal A Simple Simple MethodPretty, to Model Model a Continuous Continuous Glucose Monitoring Signal Felicity Thomas, * Christopher * Jennifer Dickson, * Matthew Signal,* Geoffrey Shaw, ** J. Geoffrey Chase* A Simple Method to Model a Continuous Glucose Monitoring Signal Felicity Thomas, * Christopher Pretty, * Jennifer Dickson, * Matthew Signal,* Geoffrey Shaw, ** J. Geoffrey Chase*
Felicity Thomas, Thomas, ** Christopher Christopher Pretty, Pretty, ** Jennifer Jennifer Dickson, Dickson, ** Matthew Matthew Signal,* Signal,* Geoffrey Geoffrey Shaw, Shaw, ** ** J. J. Geoffrey Geoffrey Chase* Chase* Felicity * Matthew * Department Mechanical Engineering, University of Geoffrey Canterbury, Felicity Thomas, * Christopher Pretty, *ofJennifer Dickson, Signal,* Shaw, ** J. Geoffrey Chase* ** Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand (e-mail: [email protected]). of Engineering, University of * Department Department of Mechanical Mechanical Engineering, University Hospital, of Canterbury, Canterbury, Christchurch, New Zealand (e-mail: [email protected]). ** Department of Intensive Care, Christchurch Christchurch, Zealand (e-mail: [email protected]). * Department New of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand (e-mail: [email protected]). ** DepartmentChristchurch, of Intensive Care, Christchurch Hospital, New Zealand ** of Care, Christchurch Hospital, Christchurch, New Zealand (e-mail: [email protected]). ** Department Department of Intensive Intensive Care, Christchurch Hospital, Christchurch, New Zealand New Zealand ** DepartmentChristchurch, of Intensive Care, Christchurch Hospital, Christchurch, New Zealand Christchurch, New Zealand Abstract: Before continuous glucose monitoring (CGM) can be safely used to guide glycaemic control Abstract: Before glucose monitoring (CGM) can safely used to guide glycaemic control (GC) protocols thecontinuous impact of suboptimal accuracy resulting frombe error or delay in calibration measurement, Abstract: Before continuous glucose monitoring (CGM) can be safely used to guide control Abstract: Before continuous glucose monitoring (CGM) can beerror safely used to calibration guide glycaemic glycaemic control (GC) protocols the impact of suboptimal accuracy resulting from or delay in measurement, sensor drift, and delayed glucose diffusion must first be characterised. Characterising this error allows (GC) protocols the impact of suboptimal accuracy resulting from error or delay in calibration measurement, Abstract: Before continuous glucose monitoring (CGM) can be safely used to guide glycaemic control (GC) protocols the impact of suboptimal accuracy resulting from error or delay in calibration measurement, sensor drift, and delayed glucose diffusion must first be characterised. Characterising this error allows models to be formed so in-silico simulations can test the performance and safety of CGM driven glycaemic sensor drift, and glucose diffusion must first be characterised. Characterising this error allows (GC) protocols thedelayed impact of suboptimal accuracy resulting from error or delay in calibration sensor and delayed glucose diffusion must first be characterised. Characterising thismeasurement, error allows models to be formed in-silico simulations can test the performance and safety of CGM driven glycaemic control drift, protocols andso examine best and worst scenarios. Existing models of CGM dynamics are now 10 models to be formed so in-silico simulations can test the performance and safety of CGM driven glycaemic sensor drift, and delayed glucose diffusion must first be characterised. Characterising this error allows models to be formed so in-silico simulations can test the performance and safety of CGM driven glycaemic control protocols and examine best and worst scenarios. Existing models of CGM dynamics are now 10 years old and significant advances in sensor technology mean the level of error produced by these models control protocols and examine best and worst scenarios. Existing models of CGM dynamics are now 10 models to be formed in-silicobest simulations canscenarios. test the performance and safety of CGM drivenare glycaemic control protocols andsoexamine Existing models of CGM dynamics now 10 years old and significant advances inand sensor technology mean the level of error produced by these models no longer characterises the dynamics ofworst more recent CGM devices. Therefore, this paper presents and years old and significant advances sensor technology mean the level of error produced by these models control protocols and examine bestin and worst scenarios. Existing models of CGM dynamics are now 10 years old and significant advances in sensor technology mean the level of error produced by these models no longer characterises the dynamics of more recent CGM devices. Therefore, this paper presents and validates a simple CGM error model based on the latest available CGM devices, as well as a generalisable no longer characterises dynamics of more recent CGM this paper presents and years old and significantthe advances in sensor technology meandevices. the levelTherefore, of error produced by these models no longer characterises the dynamics of more recent CGM devices. Therefore, this paper presents and validates aa simple CGM error model based on the latest available CGM devices, as well as a generalisable sensor modeling approach. validates simple CGM error model on latest available CGM devices, well as no longer of more recent devices. presents and validates a characterises simpleapproach. CGM the errordynamics model based based on the the latestCGM available CGMTherefore, devices, as asthis wellpaper as aa generalisable generalisable sensor modeling sensor modeling approach. validates a simple CGM error model based on the latest available CGM devices, as well as a generalisable sensor modeling approach. The model was created using 28 data sets from an observational pilot study of CGM in patients admitted sensor modeling approach. The model was created using 28 data sets from an observational pilot study of CGM in patients admitted to the Christchurch Hospital ICU during 2014-15. The model was characterised by empirical models of The was created using 28 data sets from observational pilot study of CGM in patients admitted Thethemodel model was Autocorrelation created using ICU 28was data sets2014-15. fromtoan anvalidate observational pilot study of CGM in patientsmodels admitted to Christchurch Hospital during The model was characterised by empirical of drift and noise. then used the modelled data with the measured data. The to Christchurch Hospital during The was characterised by empirical of Thethe was created using ICU 28 data sets2014-15. from an observational pilot study of CGM in patientsmodels admitted to themodel Christchurch Hospital ICU during 2014-15. The model model was characterised by empirical models ofa drift and noise. Autocorrelation was then used to validate the modelled data with the measured data. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with drift and noise. Autocorrelation was then used to validate the modelled data with the measured data. The to the Christchurch Hospital ICU during 2014-15. The model was characterised by empirical models of drift and noise. Autocorrelation was then used to validate the modelled data with the measured data. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with aa range ofabsolute 0noise. – 0.13. Hence, thebetween model is judged to be suitablethefor use in simulation totheprovide better insight median difference modelled and measured SG autocorrelation values was 0.007 with drift and Autocorrelation was then used to validate modelled data with measured data. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with a range of 0 – 0.13. Hence, the model is judged to be suitable for use in simulation to provide better insight into using toHence, guide the GC will effect control and its safety and performance. The overall modelling range of 0 ––CGM 0.13. model is judged to be suitable for in simulation to provide insight median difference between and measured SGuse autocorrelation was better 0.007 with a range ofabsolute 0 data 0.13. Hence, the model ismodelled judged to beand suitable for use inperformance. simulation values toThe provide better insight into using CGM to guide GC will effect control its safety and overall modelling process is driven and readily generalised to any other device. into guide GC will effect control its and overall modelling range of 0 –CGM 0.13.to the is judged to beand suitable for use simulation toThe provide better insight into using using CGM toHence, guide GCmodel willgeneralised effect control and its safety safety andinperformance. performance. The overall modelling process is data driven and readily to any other device. process is data driven and readily generalised to any other device. into using CGM to guide GC will effect control and its safety and performance. The overall modelling © 2017, is IFAC (International Federation of Automatic HostingIdentification by Elsevier Ltd.and All rights reserved. process data driven and readily generalised tosignal anyControl) other device. Keywords: Developments in measurement, processing, validation, Error process is data drivenseries and readily generalised tosignal any other device. Keywords: Developments in measurement, processing, Identification and validation, Error Healthcare management, disease control, critical care quantification, Time modelling, Keywords: Developments Developments in in measurement, measurement, signal signal processing, processing, Identification Identification and and validation, validation, Error Error Keywords: Healthcare management, disease control, critical care quantification, Time series modelling, Healthcare management, disease control, critical care quantification, Time series modelling, Keywords: Developments in measurement, signal processing, Identification and validation, Error disease control, care quantification, Time series modelling, Healthcare management, BG control must firstcritical be quantified and understood. 1. INTRODUCTION disease control, critical care quantification, Time series modelling, Healthcare management, BG control must first be quantified andprotocols understood. Subsequently, their interaction with GC and BG control must first be and understood. 1. INTRODUCTION INTRODUCTION BG control must first be quantified quantified andprotocols understood. Subsequently, their interaction with GC and resulting impact on performance and safety can be assessed. Two in-silico studies1. et al., 2010, Mombaerts et al., Subsequently, 1. (Signal INTRODUCTION their interaction with GC and BG control must first be quantified andprotocols understood. Subsequently, their interaction with GCcan protocols and 1. INTRODUCTION resulting impact on performance and safety be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., 2015) and a recent pilot observational trial (Signal et al., 2013) resulting impact on performance safety be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., Subsequently, their interactionand with GCcan protocols and resulting impact on performance and safety can be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., 2015) shown and aa recent recent pilot observational trialmonitoring (Signal et et al., al.,(CGM) 2013) Despite significant outpatient use and promise for CGM have that continuous glucose 2015) and pilot observational trial (Signal 2013) resulting impact on performance and safety can be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., 2015) shown and a recent pilot observational trialmonitoring (Signal et al.,(CGM) 2013) Despite significant outpatient use andKlonoff, promise 2005b) for CGM CGM have that continuous glucose (Breton et al., 2008,outpatient Klonoff, use 2005a, the devices, when coupled with a well-designed glycaemic control significant and promise for have that continuous glucose 2015) shown and a recent pilot observational trialmonitoring (Signal et al.,(CGM) 2013) Despite Despite significant outpatient use and promise for CGM have shown that continuous glucose monitoring (CGM) (Breton et al., 2008, Klonoff, 2005a, Klonoff, 2005b) the devices, when coupled with a well-designed glycaemic control literature contains very few reports of error models derived (GC) protocol, offer several potential benefits over the (Breton et al., 2008, Klonoff, 2005a, Klonoff, 2005b) the devices, when coupled with a well-designed glycaemic control Despite significant outpatient use andKlonoff, promise 2005b) for CGM have shown that continuous glucose monitoring (CGM) (Breton et al., 2008, Klonoff, 2005a, the devices, when coupled with a well-designed glycaemic control literature contains very few reports of error models derived (GC) protocol, offer several potential benefits over the from clinical sensor glucose (SG) data. Without a good model standard practice of intermittent blood glucose (BG) literature very few reports of error models derived (GC) protocol, offer several potential benefits over the (Breton etcontains al., 2008, Klonoff, 2005a, Klonoff, 2005b) the devices, when coupled with a well-designed glycaemic control literature contains very few reports of error models derived (GC) protocol, offer several potential benefits over the from clinical sensorthe glucose (SG) of data. Without a good good model standard practice of intermittent intermittent blood devices glucosehave (BG) of CGM dynamics feasibility CGM combined with GC monitoring. Theseoffer studies have shown CGM the from clinical sensor glucose (SG) data. Without a model standard practice of blood glucose (BG) literature contains very few reports of error models derived (GC) protocol, several potential benefits over the from clinical sensorthe glucose (SG)Two data. Without a good model standard practice of intermittent blood BG glucose (BG) of CGM dynamics feasibility of CGM combined with GC monitoring. Thesehypoglycaemia, studies have shown shown CGM devices have the of cannot bedynamics assessed in-silico. studies have provided ability to reduce maintain control, and CGM feasibility CGM combined with GC monitoring. These studies have CGM have the from clinical sensorthe glucose (SG) of data. Without a good model standard practice of intermittent blood devices glucose (BG) of CGM dynamics the feasibility of CGM combined with GC monitoring. These studies have shown CGM devices have the cannot be assessed in-silico. Two studies have provided ability to reduce hypoglycaemia, maintain BG control, and sufficient details of CGM device error characteristics to allow reduce nurse workload. assessed studies have provided ability to reduce maintain control, of CGMbe dynamics thein-silico. feasibilityTwo of CGM combined with GC monitoring. Thesehypoglycaemia, studies have shown CGM BG devices have and the cannot cannot be assessed in-silico. Two studies have provided ability to reduce hypoglycaemia, maintain BG control, and sufficient details of CGM CGM device error error characteristics to allow allow reduce nurse nurse workload. workload. models to beassessed created or reproduced for studies use in-silico et of device characteristics to reduce cannot bedetails in-silico. Two have (Breton provided ability to reduce hypoglycaemia, maintain BG control, and sufficient sufficient details of CGM device error characteristics to allow reduce nurse workload. models to be created or reproduced for use in-silico (Breton et al., 2008, Goldberg et al., 2004). However, these models are Typical glycaemic control protocols require BG measurements models to be created or reproduced for use in-silico (Breton et sufficient details of CGM device error characteristics to allow reduce nurse workload. models to be created or reproduced for use in-silico (Breton et al., 2008, Goldberg et al., 2004). However, these models are Typical glycaemic control protocols require BG measurements 10to be years oldetorand significant advances in sensor every 1-4 hours (Evans etprotocols al., 2012, Lonergan et al., 2006, now al., 2008, Goldberg al., 2004). However, these models are Typical glycaemic control require BG measurements models created reproduced for use in-silico (Breton et al., 2008, Goldberg etlevel al., 2004). However, these models are Typical glycaemic controlet protocols require BG resulting measurements now 10 years old and significant advances in sensor every 1-4 hours (Evans et al., 2012, Lonergan et al., 2006, technology mean the of error produced by these models Plank et al., 2006, Blaha al., 2009), typically in ~6 now 10 years old significant advances in sensor every hours (Evans al., 2012, Lonergan et al., 2006, al., 2008, Goldberg et and al., 2004). However, these models are Typical1-4 glycaemic controlet protocols require BG measurements now 10 years old and significant advances in sensor every 1-4 hours (Evans et al., 2012, Lonergan et al., 2006, technology mean the the level level ofdynamics error produced produced by these these models Plank et al., al., 2006, 2006, Blaha et al., al., 2009), typically resulting in incan ~6 technology no longer characterises theof ofadvances more recent CGM - 14 blood draws a day per patient. This frequency mean error by Plank et Blaha et typically resulting ~6 10 years and in models sensor every 1-4al.,hours (Evans et al., al.,2009), 2012, Lonergan et al., 2006, technology mean old thethis level ofsignificant error produced by these models Plank et 2006, Blaha et 2009), typically resulting incan ~6 now no longer characterises the dynamics of more recent CGM -- 14 14 blood blood draws a day per patient. This frequency devices. Therefore, paper presents and validates a simple represent a measurable part of total nurse workload (Carayon longer characterises the of recent CGM draws aa day per patient. This frequency technology mean the level ofdynamics error produced by these models Plank et al., 2006, Blaha et al., 2009), typically resulting incan ~6 no no longer characterises the dynamics of more more recent CGM - 14 blood draws day per patient. This frequency can devices. Therefore, this paper presents and validates a simple represent a measurable part of total nurse workload (Carayon CGM error model based on the latest available CGM devices. et al., 2005, Holzinger et al., 2005). CGM devices have the this paper presents and validates aa simple represent aa measurable part of total nurse workload (Carayon no longerTherefore, characterises the dynamics of more recent CGM - 14 blood draws a day per patient. This frequency can devices. devices. Therefore, this paper presents and validates simple represent measurable part of total nurse workload (Carayon CGM error error model model based based on on the the latest latest available available CGM CGM devices. devices. et al., al., 2005, 2005,toHolzinger Holzinger et al., al.,reduce 2005). the CGMnumber devices have have the CGM potential drastically of BG et et 2005). CGM devices the devices. Therefore, this paper presents and validates a simple represent a measurable part of total nurse workload (Carayon et al., 2005,toHolzinger et al.,reduce 2005). CGMnumber devices have the CGM error model based on the latest available CGM devices. potential drastically the of while BG measurements per day, positively impacting workload, potential drastically the of BG on the& latest available CGM devices. et al., 2005,to Holzinger et al.,reduce 2005). CGMnumber devices have the CGM error model 2. based PATIENTS METHODS potential to drastically reduce the number of BG measurements per day,safety positively impactingtime workload, while also improving patient and increasing in theofdesired measurements per day, positively impacting workload, while potential to drastically reduce the number BG 2. PATIENTS & METHODS measurements day,safety positively impactingtime workload, while 2. also improving patient and increasing increasing in the the desired BG target band.per 2. PATIENTS PATIENTS & & METHODS METHODS also improving patient and in measurements per day,safety positively impactingtime workload, while 2.1 Patients also improving patient safety and increasing time in the desired desired 2. PATIENTS & METHODS BG target band. BG target band. also target improving patient safety and increasing time in the desired 2.1 Patients Patients BG band. However, CGM devices tend to have suboptimal accuracy 2.1 ThisPatients study uses data from an observational pilot study of CGM 2.1 BG target band. However, CGMerror devices tend to toin have have suboptimal accuracy This 2.1 Patients This study uses uses data from from anChristchurch observationalHospital pilot study study ofduring CGM resulting from or delay calibration measurement, in patients admitted to thean ICUof However, CGM devices tend suboptimal accuracy study data observational pilot CGM However, CGM devices tend toindiffusion have suboptimal accuracy This studyAll uses data from anrecruited observational pilot study of CGM resulting from error or delay calibration measurement, in patients admitted to the Christchurch Hospital ICU during sensor drift, and delayed glucose (O’Sullivan et al., 2014-15. patients were by a physician in the ICU resulting from or delay calibration measurement, in patients admitted to the ICU However, CGMerror devices tend toin have suboptimal accuracy This study uses data from anChristchurch observationalHospital pilot study ofduring CGM resulting from error or delay in calibration measurement, in patients admitted to the Christchurch Hospital ICU during sensor drift, and delayed glucose diffusion (O’Sullivan et al., 2014-15. All patients were recruited by a physician in the ICU 2007, Heath et al., 1983). Thus, before CGM can become and informed written consent obtained. If the patient was sensor drift, and delayed (O’Sullivan et 2014-15. patients by physician in ICU resulting from error or glucose delay indiffusion calibration measurement, in patientsAll admitted towere the recruited Christchurch ICU during sensor Heath drift, and delayed glucose diffusion (O’Sullivan et al., al., 2014-15. All patients were recruited by aa Hospital physician in the the ICU 2007, et al., 1983). Thus, before CGM can become and informed written consent obtained. If the patient was ubiquitous in the care of critically ill patients these errors on unable to consent next of kin were approached for consent and 2007, et al., 1983). Thus, before CGM can become informed written consent obtained. If patient was sensor Heath drift, and delayed glucose (O’Sullivan et al., and 2014-15. All patients were recruited by a physician in the ICU 2007, Heath et al., 1983). Thus,diffusion before CGM canerrors become and informed written consent obtained. If the the patient was ubiquitous in the care of critically ill patients these on unable to consent next of kin were approached for consent and ubiquitous in the care of ill these on to next kin approached for consent and 2007, Heath Thus, before CGM canerrors become and informed written consent obtained. If the ubiquitous in et theal., care1983). of critically critically ill patients patients these errors on unable unable to consent consent next of of kin were were approached for patient consent was and ubiquitous in theIFAC care of critically ill patients these errors on9109Hosting unable to nextAll of rights kin were approached for consent and Copyright 2017 2405-8963 © 2017, IFAC (International Federation of Automatic Control) by consent Elsevier Ltd. reserved. Peer review©under of International Federation of Automatic Copyright 2017 responsibility IFAC 9109Control. Copyright © 2017 IFAC 9109 10.1016/j.ifacol.2017.08.1736 Copyright © 2017 IFAC 9109 Copyright © 2017 IFAC 9109
Proceedings of the 20th IFAC World Congress 8776 Felicity Thomas et al. / IFAC PapersOnLine 50-1 (2017) 8775–8780 Toulouse, France, July 9-14, 2017
follow up consent was obtained from the patient at a later date if applicable. Inclusion criteria were: Two consecutive BG measurements greater than 8 mmol/L, indicating the need for insulin therapy using the STAR protocol (Evans et al., 2012) Expected admission of at least 3 days Over 18 years of age A platelet count > 30,000/mL. Patients were excluded if they were not expected to survive, receiving hydroxyurea, pregnant, and/or lacked clinical equipoise. This study and use of data was approved by the Upper South A Regional Ethics Committee, New Zealand (URA/12/02/004). Table 1 shows the patient demographics. Table 1. Patient demographics displayed as median [IQR] where appropriate. APACHE II = Acute Physiology and Chronic Health Evaluation II. Patients Ages (years) Sex (M/F) APACHE II score Outcome (L/D)
21 60 [55 – 68] 11/9 20 [16 – 25] 14/7
All patients were monitored for a period of up to 3 days using the Sentrino monitoring system (Medtronic, MiniMed, Northridge, California). Patients had either one abdomen and one thigh sensor, two abdomen sensors, or one thigh sensor inserted by a trained clinician, depending on which trial phase they were enrolled in. Calibration BG measurements were obtained by specifically trained ICU nurses at least 3 times per day as recommended by the device manufacturer (MiniMed, 2014). BG measures were obtained using the Roche Accu-chek Inform II (F. Hoffmann-La Roche Ltd, Basle, Switzerland) hospital grade glucose meters as is standard practice in the Christchurch ICU, with blood typically obtained from an arterial line. CGM devices were strictly not used for determining treatment for GC during this study.
Table 2: Data used for modelling and validation No. SG signals No. SG hours No. Calibration measurements No. Reference measurements 2.3 Model development The error in a CGM signal can be broken down into separate parts specifically, the true BG signal noise and drift: 𝐶𝐶𝐶𝐶𝐶𝐶 = 𝐵𝐵𝐵𝐵𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
(1)
Where noise is the random error centred about 0 and drift is a linear bias between calibration measurements. Noise and drift were modelled based on clinical Sentrino data to create a CGM model with outputs added to reference blood glucose values to simulate the impact of CGM error on GC results. A constant drift rate with a linear bias, was assumed for the drift model, based on clinical observation and prior data. Drift was defined as the rate of increase in discrepancy between CGM signal and calibration BG measurements. The drift profile between any two calibration BG measurements was then defined by delta, the accumulated drift magnitude. The magnitude of accumulated drift between any two calibration BGs was found by measuring the size of the bias (CGM value – Calibration BG) at the second calibration BG as shown in Figure 1. Once delta is identified for each calibration measurement it can be removed from the SG for further analysis. This calculation resulted in a new drift-corrected CGM profile as shown in Figure 1.
Accumulated drift, deltai+1
In addition to BG measurements used for calibration of SG data, each patient had intermittent BG monitoring every few hours. The STAR protocol requires, on average, 12-14 BG measurements per day to guide insulin/nutrition therapy (Fisk et al., 2012). These additional reference measurements can be used to assess CGM accuracy. Each SG signal was treated separately for modelling purposes. Three patients were excluded from the analysis, Patients 17, 21 and 24. These patients had early sensor failure and were deemed clinically unsuitable for replacement sensors. In each case, not enough data was collected from these patients to be relevant to the model. Additionally, any data characteristic of a failed sensor or uncharacteristic of a sensor signal was removed, shown in Appendix A. This removal resulted in 28 separate SG signals for analysis. Table 2 summarises the data used for modelling and validation.
28 1689 380 669
Accumulated drift, deltai
Fig 1. Example of accumulated drift in a SG signal and a SG signal once drift is removed The sections between each calibration measurement were considered independently because calibration should correct for any drift. Autocorrelation of the delta data shows no tendency for a sensor to repeatedly drift in the same direction, as shown in Figure 2. Autocorrelation is the dot product of the signal after it has been shifted in time by some amount. The
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resultant angle, θ, shows the trend similarity between two vectors and its cosine has values from -1 and +1 demonstrating opposing to complete agreement. A lag window of up to 10 minutes was considered. Therefore, the similarity of the signal to itself was compared every minute from 10 minutes before to 10 minutes after the current time. The delta data was first mean shifted before autocorrelation was applied to remove bias.
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appearance of the CGM signal. High frequency noise represents electrical noise, random variation induced by the imperfect reading and transmission of the sensor signal. High frequency noise is very small in magnitude thus does not affect the identification of low frequency noise. A simple model was created using the CGM data by calculating the size of the changes in glucose from sample to sample (every minute). The sample-to-sample change was then halved to obtain an amplitude because noise is assumed to be zero mean so sample-to-sample changes would double the amplitude found over many measurements. Thus, it yields an independent, random added noise with sample-to-sample changes similar to those observed in the empirical data. 2.4 Model development To ensure the CGM model produced similar dynamics to the CGM sensors, the 28 data sets containing true reference and calibration BGs provided the framework to generate modelled SG signals. The reference and calibration BGs were linearly interpolated to give a 'true BG signal'. CGM drift, and noise are added to this ‘true BG signal’, as shown in subplot A of Figure 3. A
Fig 2. The autocorrelation of the delta drift data over a lag window of +10 and -10 minutes, for all data points. There is no correlation evident within this window. B An empirical model of drift was implemented from the cumulative distribution function (CDF) of the delta data across the entire cohort using inverse transform sampling. This method is implemented by interpolating the CDF to 100,000 points to ensure a smooth curve. A uniform random number generator then selects a value in the range 0 – 1 which was then used to obtain the corresponding interpolated CDF delta value. The process can be repeated resulting in a dataset that has the same distribution as per the empirical data.
C
D
Sensor noise contributes the remaining zero mean, random error to the modelled CGM signal of Equation 1. Noise was split into two components, low and high frequency noise. Low frequency noise is considered “the long duration” sensor noise, or, in this case, the difference between reference BG and the SG once drift is removed. High frequency noise is the “minute to minute” noise that gives the SG signal a jagged appearance. The low frequency noise was considered to be the difference between each independent reference BG and the driftcorrected SG signal. Low frequency noise accounts for the error that occurs intermittently over longer time periods, which could be induced by events such as turning or other accidental pressure applications on the sensor site (Helton et al., 2011a, Helton et al., 2011b). As was done for the drift data, an empirical model was generated from a CDF of low frequency noise by inverse sampling. Unlike low frequency sensor noise, high frequency sensor noise occurs minute-to-minute and results in the 'jagged'
E
Fig 3. Example of the process undertaken to model a SG signal. First the BG measurements are interpolated, A. Then drift, low frequenacy and high frenquency error are found by sampling from their emperical distributions, B, D and C respectively. Finally, the error is added to the interpolated BG to prove the simulated signal, E. A drift profile was then created using the empirical drift model to randomly generate a drift delta value for each 8 hour calibration interval, as shown in subplot B of Figure 3. A low frequency noise profile created by sampling every 160 minutes from the low frequency error model. Samples were taken at 160 min intervals as opposed to at the time of reference BG
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measurements because some data sets contained infrequent reference BG measurements and the mean reference measurement interval across the available dataset was 160 minutes. Consecutive samples were linearly interpolated and a median filter was used to smooth the error signal, as shown in subplot C of Figure 3, where the median filtering removes the uncharacteristic sharp edges introduced by the linear interpolation between the error points. Finally, a high frequency noise profile was generated every minute by randomly sampling from the empirical high frequency model, as shown in subplot D of Figure 3. The summed result of each component yields a simulated true BG with CGM error, as shown in Figure 3 subplot E.
trends to those displayed by the measured data. Measured SG is less tightly correlated than the median modelled SG in the majority of cases. However, only 3/28 measured SG values (A, B and C in Figure 5) do not sit within the range of modelled SG across all of the 20 minute (+/- 10 minute) windows and the median difference between the modelled and measured SG correlation values was 0.007 with a range of 0 – 0.13, the biggest differences occurring at the +10 or -10 minute time shift, where correlation might generally be expected to be weaker given the time difference from the original model.
The overall model development method is general and data driven. The use of drift and random errors is general, as these can occur in any such device, and if they don’t, they are essentially set to zero by their absence. Thus, given data from another sensor, a similar model could be generated and similarly tested and validated. 2.5 Model Validation The CGM model is a created using random process. Therefore, it cannot be deterministically compared to actual measured CGM data and, importantly, no two uses of the model for the same true BG data yield the same result. Thus, to validate the modelled signals, autocorrelation was used to assess the similarity of the simulated CGM signals to the original CGM data. All signals were first mean shifted to remove bias before autocorrelation was applied. If the resulting autocorrelation coefficients of the simulated SG and real SG are similar then the model can be considered to provide a realistic approximation of the sensor dynamics. The auto-correlation coefficients can be statistically assessed over several runs of the model for any given real SG trace. A total of 50 model-derived SG signals were simulated for each patient and the autocorrelation coefficient was calculated between the real SG and each simulated SG signal over a +10 mins to -10 mins window. The median and range of correlation coefficients of the modelled SG was then compared to the correlation coefficient of the measured SG. The closer the agreement between the correlation coefficients of the simulated signals, and the correlation coefficient of the real CGM signal the better the model. 3. RESULTS & DISCUSSION Visually and qualitatively, the CGM model generates similar signals to the empirical data. An example signal is shown in Figure 4 with real SG and 3 simulated signals. In particular, it is difficult to distinguish the real CGM signal from the modelled signals. Figure 5 displays the median and range of autocorrelation values for each time lag for each patient’s modelled SG signals. The modelled SG show very similar autocorrelation
Fig. 4. Comparing the original SG signal to that of three different modelled signals using the CGM modelled generated from empirical data
The SG of the three instances (A, B and C in Figure 5) where the measured SG autocorrelation does not fall within the range of modelled SG autocorrelation for all time lags are shown in Figure 6. It is evident the lack of agreement is most likely due to individual cases where the sensor did not behave as expected. Thus, in these limited cases, the behaviour of the sensor as seen in the data cannot be easily explained by the noise and error types defined. In this figure, subplot A corresponds to the A in Figure 5 and the high frequency noise has increased noticeably about halfway through the signal which is not seen in any of the other 28 SG signals. Subplot B corresponds to the SG of Figure 6B. The sensor glucose has many small unusual spikes uncharacteristic of the other sensors. Subplot C corresponds to Figure 6C where there is a large drop out at 300 minutes in SG compared to an otherwise stable signal with some strange spikes. Additionally, over all patients sensor glucose is very tightly correlated in both measured and modelled SG. This result is logical as the rate of which blood glucose can change is physiologically limited and under normal conditions blood glucose will be related over a short time period, such as 10 minutes. However, if the time lag is extended to ±20 or ±30 minutes the correlation coefficients of both the modelled SG and measured SG reduce, as expected.
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3.1 Limitations
A
This analysis is limited by only have 28 data sets to generate the model from. A larger cohort would provide more data to generate the empirical models from. However, the consistency of the autocorrelation coefficients of the simulated signals to the real SG value indicates there is enough data to provide an acceptable model. Equally, as more data is aggregated from any given sensor type in use, the modeling methodology is more than general enough to be updated as required, Notably, the same updating approach would also apply as sensors improve over different design changes and sensor generations. An equally applicable aspect of the model and its ability to update would include the ability to see, by tracking sensor data in use, if sensor performance changed, for better or worse. Such changes can occur, for one example, due to changes in design or manufacturing that impact sensor performance directly or in clinical use.
B
C Fig 5. Comparing the autocorrelation coefficients for the real SG to the median and range correlation coefficients of the modelled SG. A, B, and C are where the measured SG autocorrelation does not fall within the range of modelled SG autocorrelation.
A further limitation is the limited choice of noise/error types. However, the 3 choices cover most variations observed clinically without adding extra complexity and unnecessary dynamics. Finally, this model is limited by the fact it is data driven, not a dynamic, deterministic model. The benefits of this method are that it simplifies the process of calculating exact dynamic and electronic, physiological and other noise causes/sources. 3. CONCLUSIONS The CGM error model generated using the Sentrino data provides a realistic SG signal. Only 3 of 28 measured SG values do not sit with in the range of modelled SG across the entire 20 minute window considered. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with a range of 0 – 0.13. Hence, the model is judged to be suitable for use in simulation to provide better insight into using CGM to guide GC will effect control and its safety and performance. The overall modelling process is data drive and readily generalised to any other CGM.
A
B
REFERENCES C
Fig 6. The sensor glucose for the three instances where the autocorrelation range of the modelled SG does not include the autocorrelation of the measured SG for all time lags. A, B and C correspond to the A, B and C of Figure 5.
Blaha, J., Kopecky, P., Matias, M., Hovorka, R., Kunstyr, J., et al. (2009). Comparison of three protocols for tight glycemic control in cardiac surgery patients. Diabetes Care, 32, 5, 757-61. Breton, M. & Kovatchev, B. (2008). Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors. J Diabetes Sci Technol, 2, 5, 853-862. Carayon, P. & Gurses, A. (2005). A human factors engineering conceptual framework of nursing workload and patient safety in intensive care units. Intensive Crit Care Nurs, 21, 5, 284-301. Evans, A., Le Compte, A., Tan, C. S., Ward, L., Steel, J., et al. (2012). Stochastic Targeted (STAR) Glycemic Control:
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Design, Safety, and Performance. Journal of Diabetes Science and Technology, 6, 1, 102-115. Fisk, L., Lecompte, A., Penning, S., Desaive, T., Shaw, G., et al. (2012). STAR Development and Protocol Comparison. IEEE Trans Biomed Eng, 59, 12, 3357-3364. Goldberg, P. A., Siegel, M. D., Russell, R. R., Sherwin, R. S., Halickman, J. I., et al. (2004). Experience with the continuous glucose monitoring system in a medical intensive care unit. Diabetes Technol Ther, 6, 3, 339-47. Heath, G., Gavin, J., Hinderliter, J., Hagberg, J., Bloomfield, S., et al. (1983). Effects of exercise and lack of exercise on glucose tolerance and insulin sensitivity. Journal of Applied Physiology, 55, 2, 512-517. Helton, K. L., Ratner, B. D. & Wisniewski, N. A. (2011a). Biomechanics of the sensor-tissue interface-effects of motion, pressure, and design on sensor performance and foreign body response-part II: examples and application. J Diabetes Sci Technol, 5, 3, 647-56. Helton, K. L., Ratner, B. D. & Wisniewski, N. A. (2011b). Biomechanics of the sensor-tissue interface-effects of motion, pressure, and design on sensor performance and the foreign body response-part I: theoretical framework. J Diabetes Sci Technol, 5, 3, 632-46. Holzinger, U., Kitzberger, R., Fuhrmann, V., Schenk, P., Kramer, L., et al. Year. ICU-staff education and implementation of an insulin therapy algorithm improve blood glucose control. In: 18th ESICM Annual Congress, 25–28 September 2005 2005 Amsterdam, Netherlands. Klonoff, D. C. (2005a). Continuous Glucose Monitoring: Roadmap for 21st century diabetes therapy. Diabetes Care, 28, 5, 1231-9. Klonoff, D. C. (2005b). A review of continuous glucose monitoring technology. Diabetes Technol Ther, 7, 5, 7705. Lonergan, T., Compte, A. L., Willacy, M., Chase, J. G., Shaw, G. M., et al. (2006). A pilot study of the SPRINT protocol for tight glycemic control in critically Ill patients. Diabetes Technol Ther, 8, 4, 449-62. Mombaerts, L., Thomas, F., Signal, M., Desaive, T. & Chase, J. G. (2015). Continuous Glucose Monitoring: Using CGM to Guide Insulin Therapy Virtual Trials Results. IFAC-PapersOnLine, 48, 20, 112-117. O’sullivan, S. B. & Schmitz, T. J. (2007). Physical rehabilitation: assessment and treatment Philadelphia, F. A. Davis Company. Plank, J., Blaha, J., Cordingley, J., Wilinska, M. E., Chassin, L. J., et al. (2006). Multicentric, randomized, controlled trial to evaluate blood glucose control by the model predictive control algorithm versus routine glucose management protocols in intensive care unit patients. Diabetes Care, 29, 2, 271-6. Signal, M., Fisk, L., Shaw, G. M. & Chase, J. G. (2013). Concurrent continuous glucose monitoring in critically ill patients: interim results and observations. J Diabetes Sci Technol, 7, 6, 1652-3. Signal, M., Pretty, C. G., Chase, J. G., Le Compte, A. & Shaw, G. M. (2010). Continuous glucose monitors and the burden of tight glycemic control in critical care: can they cure the time cost? J Diabetes Sci Technol, 4, 3, 625-35.
Appendix A. FIRST APPENDIX
Fig A1. The sensor glucose that was removed from 6 patients data due to being uncharacteristic of the sensor, most commonly as the result of sensor failure.
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A Simple Method to Model a Continuous Glucose Monitoring Signal IFAC PapersOnLine 50-1 (2017) 8775–8780 A Simple Method to Model a Continuous Glucose Monitoring Signal A Method to a Glucose Monitoring Signal A Simple Simple MethodPretty, to Model Model a Continuous Continuous Glucose Monitoring Signal Felicity Thomas, * Christopher * Jennifer Dickson, * Matthew Signal,* Geoffrey Shaw, ** J. Geoffrey Chase* A Simple Method to Model a Continuous Glucose Monitoring Signal Felicity Thomas, * Christopher Pretty, * Jennifer Dickson, * Matthew Signal,* Geoffrey Shaw, ** J. Geoffrey Chase*
Felicity Thomas, Thomas, ** Christopher Christopher Pretty, Pretty, ** Jennifer Jennifer Dickson, Dickson, ** Matthew Matthew Signal,* Signal,* Geoffrey Geoffrey Shaw, Shaw, ** ** J. J. Geoffrey Geoffrey Chase* Chase* Felicity * Matthew * Department Mechanical Engineering, University of Geoffrey Canterbury, Felicity Thomas, * Christopher Pretty, *ofJennifer Dickson, Signal,* Shaw, ** J. Geoffrey Chase* ** Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand (e-mail: [email protected]). of Engineering, University of * Department Department of Mechanical Mechanical Engineering, University Hospital, of Canterbury, Canterbury, Christchurch, New Zealand (e-mail: [email protected]). ** Department of Intensive Care, Christchurch Christchurch, Zealand (e-mail: [email protected]). * Department New of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand (e-mail: [email protected]). ** DepartmentChristchurch, of Intensive Care, Christchurch Hospital, New Zealand ** of Care, Christchurch Hospital, Christchurch, New Zealand (e-mail: [email protected]). ** Department Department of Intensive Intensive Care, Christchurch Hospital, Christchurch, New Zealand New Zealand ** DepartmentChristchurch, of Intensive Care, Christchurch Hospital, Christchurch, New Zealand Christchurch, New Zealand Abstract: Before continuous glucose monitoring (CGM) can be safely used to guide glycaemic control Abstract: Before glucose monitoring (CGM) can safely used to guide glycaemic control (GC) protocols thecontinuous impact of suboptimal accuracy resulting frombe error or delay in calibration measurement, Abstract: Before continuous glucose monitoring (CGM) can be safely used to guide control Abstract: Before continuous glucose monitoring (CGM) can beerror safely used to calibration guide glycaemic glycaemic control (GC) protocols the impact of suboptimal accuracy resulting from or delay in measurement, sensor drift, and delayed glucose diffusion must first be characterised. Characterising this error allows (GC) protocols the impact of suboptimal accuracy resulting from error or delay in calibration measurement, Abstract: Before continuous glucose monitoring (CGM) can be safely used to guide glycaemic control (GC) protocols the impact of suboptimal accuracy resulting from error or delay in calibration measurement, sensor drift, and delayed glucose diffusion must first be characterised. Characterising this error allows models to be formed so in-silico simulations can test the performance and safety of CGM driven glycaemic sensor drift, and glucose diffusion must first be characterised. Characterising this error allows (GC) protocols thedelayed impact of suboptimal accuracy resulting from error or delay in calibration sensor and delayed glucose diffusion must first be characterised. Characterising thismeasurement, error allows models to be formed in-silico simulations can test the performance and safety of CGM driven glycaemic control drift, protocols andso examine best and worst scenarios. Existing models of CGM dynamics are now 10 models to be formed so in-silico simulations can test the performance and safety of CGM driven glycaemic sensor drift, and delayed glucose diffusion must first be characterised. Characterising this error allows models to be formed so in-silico simulations can test the performance and safety of CGM driven glycaemic control protocols and examine best and worst scenarios. Existing models of CGM dynamics are now 10 years old and significant advances in sensor technology mean the level of error produced by these models control protocols and examine best and worst scenarios. Existing models of CGM dynamics are now 10 models to be formed in-silicobest simulations canscenarios. test the performance and safety of CGM drivenare glycaemic control protocols andsoexamine Existing models of CGM dynamics now 10 years old and significant advances inand sensor technology mean the level of error produced by these models no longer characterises the dynamics ofworst more recent CGM devices. Therefore, this paper presents and years old and significant advances sensor technology mean the level of error produced by these models control protocols and examine bestin and worst scenarios. Existing models of CGM dynamics are now 10 years old and significant advances in sensor technology mean the level of error produced by these models no longer characterises the dynamics of more recent CGM devices. Therefore, this paper presents and validates a simple CGM error model based on the latest available CGM devices, as well as a generalisable no longer characterises dynamics of more recent CGM this paper presents and years old and significantthe advances in sensor technology meandevices. the levelTherefore, of error produced by these models no longer characterises the dynamics of more recent CGM devices. Therefore, this paper presents and validates aa simple CGM error model based on the latest available CGM devices, as well as a generalisable sensor modeling approach. validates simple CGM error model on latest available CGM devices, well as no longer of more recent devices. presents and validates a characterises simpleapproach. CGM the errordynamics model based based on the the latestCGM available CGMTherefore, devices, as asthis wellpaper as aa generalisable generalisable sensor modeling sensor modeling approach. validates a simple CGM error model based on the latest available CGM devices, as well as a generalisable sensor modeling approach. The model was created using 28 data sets from an observational pilot study of CGM in patients admitted sensor modeling approach. The model was created using 28 data sets from an observational pilot study of CGM in patients admitted to the Christchurch Hospital ICU during 2014-15. The model was characterised by empirical models of The was created using 28 data sets from observational pilot study of CGM in patients admitted Thethemodel model was Autocorrelation created using ICU 28was data sets2014-15. fromtoan anvalidate observational pilot study of CGM in patientsmodels admitted to Christchurch Hospital during The model was characterised by empirical of drift and noise. then used the modelled data with the measured data. The to Christchurch Hospital during The was characterised by empirical of Thethe was created using ICU 28 data sets2014-15. from an observational pilot study of CGM in patientsmodels admitted to themodel Christchurch Hospital ICU during 2014-15. The model model was characterised by empirical models ofa drift and noise. Autocorrelation was then used to validate the modelled data with the measured data. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with drift and noise. Autocorrelation was then used to validate the modelled data with the measured data. The to the Christchurch Hospital ICU during 2014-15. The model was characterised by empirical models of drift and noise. Autocorrelation was then used to validate the modelled data with the measured data. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with aa range ofabsolute 0noise. – 0.13. Hence, thebetween model is judged to be suitablethefor use in simulation totheprovide better insight median difference modelled and measured SG autocorrelation values was 0.007 with drift and Autocorrelation was then used to validate modelled data with measured data. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with a range of 0 – 0.13. Hence, the model is judged to be suitable for use in simulation to provide better insight into using toHence, guide the GC will effect control and its safety and performance. The overall modelling range of 0 ––CGM 0.13. model is judged to be suitable for in simulation to provide insight median difference between and measured SGuse autocorrelation was better 0.007 with a range ofabsolute 0 data 0.13. Hence, the model ismodelled judged to beand suitable for use inperformance. simulation values toThe provide better insight into using CGM to guide GC will effect control its safety and overall modelling process is driven and readily generalised to any other device. into guide GC will effect control its and overall modelling range of 0 –CGM 0.13.to the is judged to beand suitable for use simulation toThe provide better insight into using using CGM toHence, guide GCmodel willgeneralised effect control and its safety safety andinperformance. performance. The overall modelling process is data driven and readily to any other device. process is data driven and readily generalised to any other device. into using CGM to guide GC will effect control and its safety and performance. The overall modelling © 2017, is IFAC (International Federation of Automatic HostingIdentification by Elsevier Ltd.and All rights reserved. process data driven and readily generalised tosignal anyControl) other device. Keywords: Developments in measurement, processing, validation, Error process is data drivenseries and readily generalised tosignal any other device. Keywords: Developments in measurement, processing, Identification and validation, Error Healthcare management, disease control, critical care quantification, Time modelling, Keywords: Developments Developments in in measurement, measurement, signal signal processing, processing, Identification Identification and and validation, validation, Error Error Keywords: Healthcare management, disease control, critical care quantification, Time series modelling, Healthcare management, disease control, critical care quantification, Time series modelling, Keywords: Developments in measurement, signal processing, Identification and validation, Error disease control, care quantification, Time series modelling, Healthcare management, BG control must firstcritical be quantified and understood. 1. INTRODUCTION disease control, critical care quantification, Time series modelling, Healthcare management, BG control must first be quantified andprotocols understood. Subsequently, their interaction with GC and BG control must first be and understood. 1. INTRODUCTION INTRODUCTION BG control must first be quantified quantified andprotocols understood. Subsequently, their interaction with GC and resulting impact on performance and safety can be assessed. Two in-silico studies1. et al., 2010, Mombaerts et al., Subsequently, 1. (Signal INTRODUCTION their interaction with GC and BG control must first be quantified andprotocols understood. Subsequently, their interaction with GCcan protocols and 1. INTRODUCTION resulting impact on performance and safety be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., 2015) and a recent pilot observational trial (Signal et al., 2013) resulting impact on performance safety be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., Subsequently, their interactionand with GCcan protocols and resulting impact on performance and safety can be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., 2015) shown and aa recent recent pilot observational trialmonitoring (Signal et et al., al.,(CGM) 2013) Despite significant outpatient use and promise for CGM have that continuous glucose 2015) and pilot observational trial (Signal 2013) resulting impact on performance and safety can be assessed. Two in-silico studies (Signal et al., 2010, Mombaerts et al., 2015) shown and a recent pilot observational trialmonitoring (Signal et al.,(CGM) 2013) Despite significant outpatient use andKlonoff, promise 2005b) for CGM CGM have that continuous glucose (Breton et al., 2008,outpatient Klonoff, use 2005a, the devices, when coupled with a well-designed glycaemic control significant and promise for have that continuous glucose 2015) shown and a recent pilot observational trialmonitoring (Signal et al.,(CGM) 2013) Despite Despite significant outpatient use and promise for CGM have shown that continuous glucose monitoring (CGM) (Breton et al., 2008, Klonoff, 2005a, Klonoff, 2005b) the devices, when coupled with a well-designed glycaemic control literature contains very few reports of error models derived (GC) protocol, offer several potential benefits over the (Breton et al., 2008, Klonoff, 2005a, Klonoff, 2005b) the devices, when coupled with a well-designed glycaemic control Despite significant outpatient use andKlonoff, promise 2005b) for CGM have shown that continuous glucose monitoring (CGM) (Breton et al., 2008, Klonoff, 2005a, the devices, when coupled with a well-designed glycaemic control literature contains very few reports of error models derived (GC) protocol, offer several potential benefits over the from clinical sensor glucose (SG) data. Without a good model standard practice of intermittent blood glucose (BG) literature very few reports of error models derived (GC) protocol, offer several potential benefits over the (Breton etcontains al., 2008, Klonoff, 2005a, Klonoff, 2005b) the devices, when coupled with a well-designed glycaemic control literature contains very few reports of error models derived (GC) protocol, offer several potential benefits over the from clinical sensorthe glucose (SG) of data. Without a good good model standard practice of intermittent intermittent blood devices glucosehave (BG) of CGM dynamics feasibility CGM combined with GC monitoring. Theseoffer studies have shown CGM the from clinical sensor glucose (SG) data. Without a model standard practice of blood glucose (BG) literature contains very few reports of error models derived (GC) protocol, several potential benefits over the from clinical sensorthe glucose (SG)Two data. Without a good model standard practice of intermittent blood BG glucose (BG) of CGM dynamics feasibility of CGM combined with GC monitoring. Thesehypoglycaemia, studies have shown shown CGM devices have the of cannot bedynamics assessed in-silico. studies have provided ability to reduce maintain control, and CGM feasibility CGM combined with GC monitoring. These studies have CGM have the from clinical sensorthe glucose (SG) of data. Without a good model standard practice of intermittent blood devices glucose (BG) of CGM dynamics the feasibility of CGM combined with GC monitoring. These studies have shown CGM devices have the cannot be assessed in-silico. Two studies have provided ability to reduce hypoglycaemia, maintain BG control, and sufficient details of CGM device error characteristics to allow reduce nurse workload. assessed studies have provided ability to reduce maintain control, of CGMbe dynamics thein-silico. feasibilityTwo of CGM combined with GC monitoring. Thesehypoglycaemia, studies have shown CGM BG devices have and the cannot cannot be assessed in-silico. Two studies have provided ability to reduce hypoglycaemia, maintain BG control, and sufficient details of CGM CGM device error error characteristics to allow allow reduce nurse nurse workload. workload. models to beassessed created or reproduced for studies use in-silico et of device characteristics to reduce cannot bedetails in-silico. Two have (Breton provided ability to reduce hypoglycaemia, maintain BG control, and sufficient sufficient details of CGM device error characteristics to allow reduce nurse workload. models to be created or reproduced for use in-silico (Breton et al., 2008, Goldberg et al., 2004). However, these models are Typical glycaemic control protocols require BG measurements models to be created or reproduced for use in-silico (Breton et sufficient details of CGM device error characteristics to allow reduce nurse workload. models to be created or reproduced for use in-silico (Breton et al., 2008, Goldberg et al., 2004). However, these models are Typical glycaemic control protocols require BG measurements 10to be years oldetorand significant advances in sensor every 1-4 hours (Evans etprotocols al., 2012, Lonergan et al., 2006, now al., 2008, Goldberg al., 2004). However, these models are Typical glycaemic control require BG measurements models created reproduced for use in-silico (Breton et al., 2008, Goldberg etlevel al., 2004). However, these models are Typical glycaemic controlet protocols require BG resulting measurements now 10 years old and significant advances in sensor every 1-4 hours (Evans et al., 2012, Lonergan et al., 2006, technology mean the of error produced by these models Plank et al., 2006, Blaha al., 2009), typically in ~6 now 10 years old significant advances in sensor every hours (Evans al., 2012, Lonergan et al., 2006, al., 2008, Goldberg et and al., 2004). However, these models are Typical1-4 glycaemic controlet protocols require BG measurements now 10 years old and significant advances in sensor every 1-4 hours (Evans et al., 2012, Lonergan et al., 2006, technology mean the the level level ofdynamics error produced produced by these these models Plank et al., al., 2006, 2006, Blaha et al., al., 2009), typically resulting in incan ~6 technology no longer characterises theof ofadvances more recent CGM - 14 blood draws a day per patient. This frequency mean error by Plank et Blaha et typically resulting ~6 10 years and in models sensor every 1-4al.,hours (Evans et al., al.,2009), 2012, Lonergan et al., 2006, technology mean old thethis level ofsignificant error produced by these models Plank et 2006, Blaha et 2009), typically resulting incan ~6 now no longer characterises the dynamics of more recent CGM -- 14 14 blood blood draws a day per patient. This frequency devices. Therefore, paper presents and validates a simple represent a measurable part of total nurse workload (Carayon longer characterises the of recent CGM draws aa day per patient. This frequency technology mean the level ofdynamics error produced by these models Plank et al., 2006, Blaha et al., 2009), typically resulting incan ~6 no no longer characterises the dynamics of more more recent CGM - 14 blood draws day per patient. This frequency can devices. Therefore, this paper presents and validates a simple represent a measurable part of total nurse workload (Carayon CGM error model based on the latest available CGM devices. et al., 2005, Holzinger et al., 2005). CGM devices have the this paper presents and validates aa simple represent aa measurable part of total nurse workload (Carayon no longerTherefore, characterises the dynamics of more recent CGM - 14 blood draws a day per patient. This frequency can devices. devices. Therefore, this paper presents and validates simple represent measurable part of total nurse workload (Carayon CGM error error model model based based on on the the latest latest available available CGM CGM devices. devices. et al., al., 2005, 2005,toHolzinger Holzinger et al., al.,reduce 2005). the CGMnumber devices have have the CGM potential drastically of BG et et 2005). CGM devices the devices. Therefore, this paper presents and validates a simple represent a measurable part of total nurse workload (Carayon et al., 2005,toHolzinger et al.,reduce 2005). CGMnumber devices have the CGM error model based on the latest available CGM devices. potential drastically the of while BG measurements per day, positively impacting workload, potential drastically the of BG on the& latest available CGM devices. et al., 2005,to Holzinger et al.,reduce 2005). CGMnumber devices have the CGM error model 2. based PATIENTS METHODS potential to drastically reduce the number of BG measurements per day,safety positively impactingtime workload, while also improving patient and increasing in theofdesired measurements per day, positively impacting workload, while potential to drastically reduce the number BG 2. PATIENTS & METHODS measurements day,safety positively impactingtime workload, while 2. also improving patient and increasing increasing in the the desired BG target band.per 2. PATIENTS PATIENTS & & METHODS METHODS also improving patient and in measurements per day,safety positively impactingtime workload, while 2.1 Patients also improving patient safety and increasing time in the desired desired 2. PATIENTS & METHODS BG target band. BG target band. also target improving patient safety and increasing time in the desired 2.1 Patients Patients BG band. However, CGM devices tend to have suboptimal accuracy 2.1 ThisPatients study uses data from an observational pilot study of CGM 2.1 BG target band. However, CGMerror devices tend to toin have have suboptimal accuracy This 2.1 Patients This study uses uses data from from anChristchurch observationalHospital pilot study study ofduring CGM resulting from or delay calibration measurement, in patients admitted to thean ICUof However, CGM devices tend suboptimal accuracy study data observational pilot CGM However, CGM devices tend toindiffusion have suboptimal accuracy This studyAll uses data from anrecruited observational pilot study of CGM resulting from error or delay calibration measurement, in patients admitted to the Christchurch Hospital ICU during sensor drift, and delayed glucose (O’Sullivan et al., 2014-15. patients were by a physician in the ICU resulting from or delay calibration measurement, in patients admitted to the ICU However, CGMerror devices tend toin have suboptimal accuracy This study uses data from anChristchurch observationalHospital pilot study ofduring CGM resulting from error or delay in calibration measurement, in patients admitted to the Christchurch Hospital ICU during sensor drift, and delayed glucose diffusion (O’Sullivan et al., 2014-15. All patients were recruited by a physician in the ICU 2007, Heath et al., 1983). Thus, before CGM can become and informed written consent obtained. If the patient was sensor drift, and delayed (O’Sullivan et 2014-15. patients by physician in ICU resulting from error or glucose delay indiffusion calibration measurement, in patientsAll admitted towere the recruited Christchurch ICU during sensor Heath drift, and delayed glucose diffusion (O’Sullivan et al., al., 2014-15. All patients were recruited by aa Hospital physician in the the ICU 2007, et al., 1983). Thus, before CGM can become and informed written consent obtained. If the patient was ubiquitous in the care of critically ill patients these errors on unable to consent next of kin were approached for consent and 2007, et al., 1983). Thus, before CGM can become informed written consent obtained. If patient was sensor Heath drift, and delayed glucose (O’Sullivan et al., and 2014-15. All patients were recruited by a physician in the ICU 2007, Heath et al., 1983). Thus,diffusion before CGM canerrors become and informed written consent obtained. If the the patient was ubiquitous in the care of critically ill patients these on unable to consent next of kin were approached for consent and ubiquitous in the care of ill these on to next kin approached for consent and 2007, Heath Thus, before CGM canerrors become and informed written consent obtained. If the ubiquitous in et theal., care1983). of critically critically ill patients patients these errors on unable unable to consent consent next of of kin were were approached for patient consent was and ubiquitous in theIFAC care of critically ill patients these errors on9109Hosting unable to nextAll of rights kin were approached for consent and Copyright 2017 2405-8963 © 2017, IFAC (International Federation of Automatic Control) by consent Elsevier Ltd. reserved. Peer review©under of International Federation of Automatic Copyright 2017 responsibility IFAC 9109Control. Copyright © 2017 IFAC 9109 10.1016/j.ifacol.2017.08.1736 Copyright © 2017 IFAC 9109 Copyright © 2017 IFAC 9109
Proceedings of the 20th IFAC World Congress 8776 Felicity Thomas et al. / IFAC PapersOnLine 50-1 (2017) 8775–8780 Toulouse, France, July 9-14, 2017
follow up consent was obtained from the patient at a later date if applicable. Inclusion criteria were: Two consecutive BG measurements greater than 8 mmol/L, indicating the need for insulin therapy using the STAR protocol (Evans et al., 2012) Expected admission of at least 3 days Over 18 years of age A platelet count > 30,000/mL. Patients were excluded if they were not expected to survive, receiving hydroxyurea, pregnant, and/or lacked clinical equipoise. This study and use of data was approved by the Upper South A Regional Ethics Committee, New Zealand (URA/12/02/004). Table 1 shows the patient demographics. Table 1. Patient demographics displayed as median [IQR] where appropriate. APACHE II = Acute Physiology and Chronic Health Evaluation II. Patients Ages (years) Sex (M/F) APACHE II score Outcome (L/D)
21 60 [55 – 68] 11/9 20 [16 – 25] 14/7
All patients were monitored for a period of up to 3 days using the Sentrino monitoring system (Medtronic, MiniMed, Northridge, California). Patients had either one abdomen and one thigh sensor, two abdomen sensors, or one thigh sensor inserted by a trained clinician, depending on which trial phase they were enrolled in. Calibration BG measurements were obtained by specifically trained ICU nurses at least 3 times per day as recommended by the device manufacturer (MiniMed, 2014). BG measures were obtained using the Roche Accu-chek Inform II (F. Hoffmann-La Roche Ltd, Basle, Switzerland) hospital grade glucose meters as is standard practice in the Christchurch ICU, with blood typically obtained from an arterial line. CGM devices were strictly not used for determining treatment for GC during this study.
Table 2: Data used for modelling and validation No. SG signals No. SG hours No. Calibration measurements No. Reference measurements 2.3 Model development The error in a CGM signal can be broken down into separate parts specifically, the true BG signal noise and drift: 𝐶𝐶𝐶𝐶𝐶𝐶 = 𝐵𝐵𝐵𝐵𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 + 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
(1)
Where noise is the random error centred about 0 and drift is a linear bias between calibration measurements. Noise and drift were modelled based on clinical Sentrino data to create a CGM model with outputs added to reference blood glucose values to simulate the impact of CGM error on GC results. A constant drift rate with a linear bias, was assumed for the drift model, based on clinical observation and prior data. Drift was defined as the rate of increase in discrepancy between CGM signal and calibration BG measurements. The drift profile between any two calibration BG measurements was then defined by delta, the accumulated drift magnitude. The magnitude of accumulated drift between any two calibration BGs was found by measuring the size of the bias (CGM value – Calibration BG) at the second calibration BG as shown in Figure 1. Once delta is identified for each calibration measurement it can be removed from the SG for further analysis. This calculation resulted in a new drift-corrected CGM profile as shown in Figure 1.
Accumulated drift, deltai+1
In addition to BG measurements used for calibration of SG data, each patient had intermittent BG monitoring every few hours. The STAR protocol requires, on average, 12-14 BG measurements per day to guide insulin/nutrition therapy (Fisk et al., 2012). These additional reference measurements can be used to assess CGM accuracy. Each SG signal was treated separately for modelling purposes. Three patients were excluded from the analysis, Patients 17, 21 and 24. These patients had early sensor failure and were deemed clinically unsuitable for replacement sensors. In each case, not enough data was collected from these patients to be relevant to the model. Additionally, any data characteristic of a failed sensor or uncharacteristic of a sensor signal was removed, shown in Appendix A. This removal resulted in 28 separate SG signals for analysis. Table 2 summarises the data used for modelling and validation.
28 1689 380 669
Accumulated drift, deltai
Fig 1. Example of accumulated drift in a SG signal and a SG signal once drift is removed The sections between each calibration measurement were considered independently because calibration should correct for any drift. Autocorrelation of the delta data shows no tendency for a sensor to repeatedly drift in the same direction, as shown in Figure 2. Autocorrelation is the dot product of the signal after it has been shifted in time by some amount. The
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resultant angle, θ, shows the trend similarity between two vectors and its cosine has values from -1 and +1 demonstrating opposing to complete agreement. A lag window of up to 10 minutes was considered. Therefore, the similarity of the signal to itself was compared every minute from 10 minutes before to 10 minutes after the current time. The delta data was first mean shifted before autocorrelation was applied to remove bias.
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appearance of the CGM signal. High frequency noise represents electrical noise, random variation induced by the imperfect reading and transmission of the sensor signal. High frequency noise is very small in magnitude thus does not affect the identification of low frequency noise. A simple model was created using the CGM data by calculating the size of the changes in glucose from sample to sample (every minute). The sample-to-sample change was then halved to obtain an amplitude because noise is assumed to be zero mean so sample-to-sample changes would double the amplitude found over many measurements. Thus, it yields an independent, random added noise with sample-to-sample changes similar to those observed in the empirical data. 2.4 Model development To ensure the CGM model produced similar dynamics to the CGM sensors, the 28 data sets containing true reference and calibration BGs provided the framework to generate modelled SG signals. The reference and calibration BGs were linearly interpolated to give a 'true BG signal'. CGM drift, and noise are added to this ‘true BG signal’, as shown in subplot A of Figure 3. A
Fig 2. The autocorrelation of the delta drift data over a lag window of +10 and -10 minutes, for all data points. There is no correlation evident within this window. B An empirical model of drift was implemented from the cumulative distribution function (CDF) of the delta data across the entire cohort using inverse transform sampling. This method is implemented by interpolating the CDF to 100,000 points to ensure a smooth curve. A uniform random number generator then selects a value in the range 0 – 1 which was then used to obtain the corresponding interpolated CDF delta value. The process can be repeated resulting in a dataset that has the same distribution as per the empirical data.
C
D
Sensor noise contributes the remaining zero mean, random error to the modelled CGM signal of Equation 1. Noise was split into two components, low and high frequency noise. Low frequency noise is considered “the long duration” sensor noise, or, in this case, the difference between reference BG and the SG once drift is removed. High frequency noise is the “minute to minute” noise that gives the SG signal a jagged appearance. The low frequency noise was considered to be the difference between each independent reference BG and the driftcorrected SG signal. Low frequency noise accounts for the error that occurs intermittently over longer time periods, which could be induced by events such as turning or other accidental pressure applications on the sensor site (Helton et al., 2011a, Helton et al., 2011b). As was done for the drift data, an empirical model was generated from a CDF of low frequency noise by inverse sampling. Unlike low frequency sensor noise, high frequency sensor noise occurs minute-to-minute and results in the 'jagged'
E
Fig 3. Example of the process undertaken to model a SG signal. First the BG measurements are interpolated, A. Then drift, low frequenacy and high frenquency error are found by sampling from their emperical distributions, B, D and C respectively. Finally, the error is added to the interpolated BG to prove the simulated signal, E. A drift profile was then created using the empirical drift model to randomly generate a drift delta value for each 8 hour calibration interval, as shown in subplot B of Figure 3. A low frequency noise profile created by sampling every 160 minutes from the low frequency error model. Samples were taken at 160 min intervals as opposed to at the time of reference BG
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measurements because some data sets contained infrequent reference BG measurements and the mean reference measurement interval across the available dataset was 160 minutes. Consecutive samples were linearly interpolated and a median filter was used to smooth the error signal, as shown in subplot C of Figure 3, where the median filtering removes the uncharacteristic sharp edges introduced by the linear interpolation between the error points. Finally, a high frequency noise profile was generated every minute by randomly sampling from the empirical high frequency model, as shown in subplot D of Figure 3. The summed result of each component yields a simulated true BG with CGM error, as shown in Figure 3 subplot E.
trends to those displayed by the measured data. Measured SG is less tightly correlated than the median modelled SG in the majority of cases. However, only 3/28 measured SG values (A, B and C in Figure 5) do not sit within the range of modelled SG across all of the 20 minute (+/- 10 minute) windows and the median difference between the modelled and measured SG correlation values was 0.007 with a range of 0 – 0.13, the biggest differences occurring at the +10 or -10 minute time shift, where correlation might generally be expected to be weaker given the time difference from the original model.
The overall model development method is general and data driven. The use of drift and random errors is general, as these can occur in any such device, and if they don’t, they are essentially set to zero by their absence. Thus, given data from another sensor, a similar model could be generated and similarly tested and validated. 2.5 Model Validation The CGM model is a created using random process. Therefore, it cannot be deterministically compared to actual measured CGM data and, importantly, no two uses of the model for the same true BG data yield the same result. Thus, to validate the modelled signals, autocorrelation was used to assess the similarity of the simulated CGM signals to the original CGM data. All signals were first mean shifted to remove bias before autocorrelation was applied. If the resulting autocorrelation coefficients of the simulated SG and real SG are similar then the model can be considered to provide a realistic approximation of the sensor dynamics. The auto-correlation coefficients can be statistically assessed over several runs of the model for any given real SG trace. A total of 50 model-derived SG signals were simulated for each patient and the autocorrelation coefficient was calculated between the real SG and each simulated SG signal over a +10 mins to -10 mins window. The median and range of correlation coefficients of the modelled SG was then compared to the correlation coefficient of the measured SG. The closer the agreement between the correlation coefficients of the simulated signals, and the correlation coefficient of the real CGM signal the better the model. 3. RESULTS & DISCUSSION Visually and qualitatively, the CGM model generates similar signals to the empirical data. An example signal is shown in Figure 4 with real SG and 3 simulated signals. In particular, it is difficult to distinguish the real CGM signal from the modelled signals. Figure 5 displays the median and range of autocorrelation values for each time lag for each patient’s modelled SG signals. The modelled SG show very similar autocorrelation
Fig. 4. Comparing the original SG signal to that of three different modelled signals using the CGM modelled generated from empirical data
The SG of the three instances (A, B and C in Figure 5) where the measured SG autocorrelation does not fall within the range of modelled SG autocorrelation for all time lags are shown in Figure 6. It is evident the lack of agreement is most likely due to individual cases where the sensor did not behave as expected. Thus, in these limited cases, the behaviour of the sensor as seen in the data cannot be easily explained by the noise and error types defined. In this figure, subplot A corresponds to the A in Figure 5 and the high frequency noise has increased noticeably about halfway through the signal which is not seen in any of the other 28 SG signals. Subplot B corresponds to the SG of Figure 6B. The sensor glucose has many small unusual spikes uncharacteristic of the other sensors. Subplot C corresponds to Figure 6C where there is a large drop out at 300 minutes in SG compared to an otherwise stable signal with some strange spikes. Additionally, over all patients sensor glucose is very tightly correlated in both measured and modelled SG. This result is logical as the rate of which blood glucose can change is physiologically limited and under normal conditions blood glucose will be related over a short time period, such as 10 minutes. However, if the time lag is extended to ±20 or ±30 minutes the correlation coefficients of both the modelled SG and measured SG reduce, as expected.
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3.1 Limitations
A
This analysis is limited by only have 28 data sets to generate the model from. A larger cohort would provide more data to generate the empirical models from. However, the consistency of the autocorrelation coefficients of the simulated signals to the real SG value indicates there is enough data to provide an acceptable model. Equally, as more data is aggregated from any given sensor type in use, the modeling methodology is more than general enough to be updated as required, Notably, the same updating approach would also apply as sensors improve over different design changes and sensor generations. An equally applicable aspect of the model and its ability to update would include the ability to see, by tracking sensor data in use, if sensor performance changed, for better or worse. Such changes can occur, for one example, due to changes in design or manufacturing that impact sensor performance directly or in clinical use.
B
C Fig 5. Comparing the autocorrelation coefficients for the real SG to the median and range correlation coefficients of the modelled SG. A, B, and C are where the measured SG autocorrelation does not fall within the range of modelled SG autocorrelation.
A further limitation is the limited choice of noise/error types. However, the 3 choices cover most variations observed clinically without adding extra complexity and unnecessary dynamics. Finally, this model is limited by the fact it is data driven, not a dynamic, deterministic model. The benefits of this method are that it simplifies the process of calculating exact dynamic and electronic, physiological and other noise causes/sources. 3. CONCLUSIONS The CGM error model generated using the Sentrino data provides a realistic SG signal. Only 3 of 28 measured SG values do not sit with in the range of modelled SG across the entire 20 minute window considered. The median absolute difference between modelled and measured SG autocorrelation values was 0.007 with a range of 0 – 0.13. Hence, the model is judged to be suitable for use in simulation to provide better insight into using CGM to guide GC will effect control and its safety and performance. The overall modelling process is data drive and readily generalised to any other CGM.
A
B
REFERENCES C
Fig 6. The sensor glucose for the three instances where the autocorrelation range of the modelled SG does not include the autocorrelation of the measured SG for all time lags. A, B and C correspond to the A, B and C of Figure 5.
Blaha, J., Kopecky, P., Matias, M., Hovorka, R., Kunstyr, J., et al. (2009). Comparison of three protocols for tight glycemic control in cardiac surgery patients. Diabetes Care, 32, 5, 757-61. Breton, M. & Kovatchev, B. (2008). Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors. J Diabetes Sci Technol, 2, 5, 853-862. Carayon, P. & Gurses, A. (2005). A human factors engineering conceptual framework of nursing workload and patient safety in intensive care units. Intensive Crit Care Nurs, 21, 5, 284-301. Evans, A., Le Compte, A., Tan, C. S., Ward, L., Steel, J., et al. (2012). Stochastic Targeted (STAR) Glycemic Control:
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Design, Safety, and Performance. Journal of Diabetes Science and Technology, 6, 1, 102-115. Fisk, L., Lecompte, A., Penning, S., Desaive, T., Shaw, G., et al. (2012). STAR Development and Protocol Comparison. IEEE Trans Biomed Eng, 59, 12, 3357-3364. Goldberg, P. A., Siegel, M. D., Russell, R. R., Sherwin, R. S., Halickman, J. I., et al. (2004). Experience with the continuous glucose monitoring system in a medical intensive care unit. Diabetes Technol Ther, 6, 3, 339-47. Heath, G., Gavin, J., Hinderliter, J., Hagberg, J., Bloomfield, S., et al. (1983). Effects of exercise and lack of exercise on glucose tolerance and insulin sensitivity. Journal of Applied Physiology, 55, 2, 512-517. Helton, K. L., Ratner, B. D. & Wisniewski, N. A. (2011a). Biomechanics of the sensor-tissue interface-effects of motion, pressure, and design on sensor performance and foreign body response-part II: examples and application. J Diabetes Sci Technol, 5, 3, 647-56. Helton, K. L., Ratner, B. D. & Wisniewski, N. A. (2011b). Biomechanics of the sensor-tissue interface-effects of motion, pressure, and design on sensor performance and the foreign body response-part I: theoretical framework. J Diabetes Sci Technol, 5, 3, 632-46. Holzinger, U., Kitzberger, R., Fuhrmann, V., Schenk, P., Kramer, L., et al. Year. ICU-staff education and implementation of an insulin therapy algorithm improve blood glucose control. In: 18th ESICM Annual Congress, 25–28 September 2005 2005 Amsterdam, Netherlands. Klonoff, D. C. (2005a). Continuous Glucose Monitoring: Roadmap for 21st century diabetes therapy. Diabetes Care, 28, 5, 1231-9. Klonoff, D. C. (2005b). A review of continuous glucose monitoring technology. Diabetes Technol Ther, 7, 5, 7705. Lonergan, T., Compte, A. L., Willacy, M., Chase, J. G., Shaw, G. M., et al. (2006). A pilot study of the SPRINT protocol for tight glycemic control in critically Ill patients. Diabetes Technol Ther, 8, 4, 449-62. Mombaerts, L., Thomas, F., Signal, M., Desaive, T. & Chase, J. G. (2015). Continuous Glucose Monitoring: Using CGM to Guide Insulin Therapy Virtual Trials Results. IFAC-PapersOnLine, 48, 20, 112-117. O’sullivan, S. B. & Schmitz, T. J. (2007). Physical rehabilitation: assessment and treatment Philadelphia, F. A. Davis Company. Plank, J., Blaha, J., Cordingley, J., Wilinska, M. E., Chassin, L. J., et al. (2006). Multicentric, randomized, controlled trial to evaluate blood glucose control by the model predictive control algorithm versus routine glucose management protocols in intensive care unit patients. Diabetes Care, 29, 2, 271-6. Signal, M., Fisk, L., Shaw, G. M. & Chase, J. G. (2013). Concurrent continuous glucose monitoring in critically ill patients: interim results and observations. J Diabetes Sci Technol, 7, 6, 1652-3. Signal, M., Pretty, C. G., Chase, J. G., Le Compte, A. & Shaw, G. M. (2010). Continuous glucose monitors and the burden of tight glycemic control in critical care: can they cure the time cost? J Diabetes Sci Technol, 4, 3, 625-35.
Appendix A. FIRST APPENDIX
Fig A1. The sensor glucose that was removed from 6 patients data due to being uncharacteristic of the sensor, most commonly as the result of sensor failure.
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